Is there a possibility to save my map in a non-vector format. I would like prevent the possibility to change my map, and also to avoid long time of loading and navigating like in a vector format. Is there any way to save it as non-vector.
Be aware: Josm is an editor to manipulate raw OSM data and to upload edited data again to the main OSM server.
If you want a map that is not editable any more, you need a bitmap result or a PDF file.
Have a look at the OSM wiki about http://wiki.openstreetmap.org/wiki/Rendering to see how you can visualize OSM data.